A family of complex nilmanifolds with infinitely many real homotopy types

Adela Latorre; Luis Ugarte; Raquel Villacampa

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arXiv · 1712.07820

A family of complex nilmanifolds with infinitely many real homotopy types

Adela Latorre·Luis Ugarte·Raquel Villacampa

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Abstract

We find a one-parameter family of non-isomorphic nilpotent Lie algebras $\mathfrak{g}_a$, with $a \in [0,\infty)$, of real dimension eight with (strongly non-nilpotent) complex structures. By restricting $a$ to take rational values, we arrive at the existence of infinitely many real homotopy types of $8$-dimensional nilmanifolds admitting a complex structure. Moreover, balanced Hermitian metrics and generalized Gauduchon metrics on such nilmanifolds are constructed.

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Adela Latorre, Luis Ugarte, Raquel Villacampa. 2017-12-21. A family of complex nilmanifolds with infinitely many real homotopy types. https://arxiv.org/abs/1712.07820

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